In the standard approach to magnetic resonance imaging one uses a strong background field that is as homogeneous as possible. Commercial MR imaging magnets are homogeneous, within the field of view, to about 1 ppm. In “open” MRI systems, the field homogeneity is somewhat less, but still in this general range. One can imagine a variety of situations where it might be useful to do magnetic resonance imaging with the object placed entirely outside the magnet's bore. As a consequence of Runge's Theorem, it is possible to design coils so that this external field is as homogeneous as one would like, in a given region of space. However, this requires a large expenditure of power and complicated, difficult to design arrangements of coils. On the other hand, with simpler arrangements of permanent magnets or electromagnets, one can produce a field, B0, such that, in a given region of space, exterior to the magnets, or coils: (1) The field is strong; (2) The direction of B0 varies in a small solid angle; (3) The level sets of |B0| are smooth; and (4) The size of ∇|B0| is not too large.
Several groups have considered problems of this sort. Generally speaking, the prior art uses pulsed gradients for spatial encoding, and refocusing pulses to repeatedly refocus the accumulating phase in the direction of the permanent gradient. These ideas are described in U.S. Pat. No. 4,656,425 to Bendel, as well as in U.S. Pat. No. 5,023,554 to Cho and Wong. The idea is further developed by Crowley and Rose as described in U.S. Pat. No. 5,304,930 and U.S. Pat. No. 5,493,225. Pulsed gradients are also used in SPRITE, though for different reasons, as noted by Balcom et al., Single-point ramped imaging with T1 enhancement (SPRITE), J. Mag. Res. A, Vol. 123 (1996), pp. 131-134.
Another group considering such problems is that of Dr. Alexander Pines at University of California at Berkeley. His work is described in the recent PNAS paper: “Three-dimensional phase-encoded chemical shift MRI in the presence of inhomogeneous fields” by Vasiliki Demas, Dimitris Sakellariou, Carlos A. Meriles, Songi Han, Jeffrey Reimer, and Alexander Pines. Their approach is somewhat different in that they try to match inhomogeneities in the B1-field with that in the B0-field in order to effectively “cancel” them out. Their efforts are more directed towards spectroscopy and they consider very small field gradients.
Still another group working on problems of this sort is that of Bernhard Blümich at RWTH Aachen in Aachen, Germany. This group's work is described in “The NMR-mouse: construction, excitation, and applications” by Blümich B, Blumler P, Eidmann G, Guthausen A, Haken R, Schmitz U, Saito K, and Zimmer G in Magn Reson Imaging. 1998, pgs 479-484. Their approach is again different from what is described herein in that it uses a stroboscopic acquisition technique. Though it is very good for spectroscopy of materials, it is too time consuming and SAR intensive for in vivo applications.
The present invention addresses methods and apparatus for imaging in such a field as described in a paper by one of the present inventors (C L Epstein) entitled “Magnetic Resonance Imaging in Inhomogeneous Fields,” Inverse Problems, Vol. 20, pages 753-780 (Mar. 19, 2004), the contents of which are hereby incorporated by reference in their entirety. Further refinements of this method are presented herein for acquiring data that lead to a fairly standard 2d-reconstruction problem.